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Counting Domino Tilings of Rectangles via Resultants

✍ Scribed by Volker Strehl

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 256 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0752

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✦ Synopsis

The classical cosine formula for enumerating domino tilings of a rectangle, due to Kasteleyn, Temperley, and Fisher, is proved once again, here using a combination of standard tools from combinatorics and algebra.

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Let t(k, n) denote the number of ways to tile a C x n rectangle with 1 x 2 rectangles (called dominoes). We show that for each fixed k the s( quence tk = (t(k, O), t(k, I), . . .) satisfies a difference equation (linear, homogeneous, and w ith constant coefficients). Furthermore, a computational met